Which solitaire games should I play?

As you get to know your way round the different games, you'll see that there
are at least a couple of factors that differentiate the games:

Overall game type. A common type is the addition or building game, in which
the aim is generally to build all cards on to a number of 'foundations', typically requiring
some degree of strategy.
On the other hand, in pair discard games the aim of the game
is to discard the entire deck by pairs of cards that meet some requirement.

How many cards are hidden vs how many are revealed at the start of the game, which can affect
the strategy/luck ratio of the game as you might expect.

The building rules for the game typically determine how difficult a game is going to
be. In a game where building is done by suit, typically more strategy will be required and
less 'room for manoeuvre' will be available compared to games where building is by colour
(red/black, as in Klondike).

If you are the kind of person that prefers a bit of strategy to pure luck, then you will
probably prefer the 'building' style games.

Bearing this in mind, some good choices to start off with are:

Klondike patience, one of the most popular variants,
still remains a good choice: it combines the 'additive' gameplay type with the more 'lax' red/black
building rule, allowing the game to come out a reasonable proportion of the time;

Scorpion, which for those preferring a bit of
strategy has the advantage that most of the cards are revealed and available for play from the start of the game;

Yukon comes highly recommended as a combination of Klondike and
Scorpion: it has a similar gameplay to Scorpion but with foundations;

Pyramid 13 is recommended as a medium-strategy game
of the 'discard' variety.

Interested in a bit of history? Trace the history of Free Cell!

Both the iPad and macOS versions of Solitaire Whizz contain versions of forerunners to the now infamous
Free Cell version (as well as some different variants of Free Cell itself). Check out:

Napoleon At St Helena (Napoleon pâ S:t Helena): the version included in the Solitaire Whizz compendium is
an implementation of Napoleon pâ S:t Helena, described in Swedish author Einar Werner's 1948
work Världens bästa Patienser och Patiensspel (pp. 60-61). The game introduces the
notion of 'store' piles (what would be referred to as the "cells" in Free Cell), but with the key difference that these
piles are populated at the start of the game.

Baker's Game: a game described by Martin Gardener in his 1968 Scientific American article
Combinatorial possibilities in a pack of shuffled cards and attributed to the father of mathematician
C. L. Baker. Crucially, the game was introduced as allowing multiple variants, and both 3 and 4-suit versions
are included in Solitaire Whizz.

Free Cell itself is included in 3 variants. (See the Free Cell
game instructions for a screenshot of the original 1978 game that would inspire the famous Windows version!)

Games not recommended for beginners

The games Beleaguered Castle and variant
Streets and Alleys are only recommended
for experienced patience players: they are in reality rather difficult and may be off-putting for
beginners!

Similarly, the two variants of Calculation are also rather difficult. They provide an
interesting challenge as something different for experienced players, but are atypical of
solitaire games in general and also likely to put off beginners.